Adaptive Fixed-time Control Research Articles

Cluster formation tracking of networked perturbed robotic systems via hierarchical fixed-time neural adaptive approach

This paper investigates the fixed-time cluster formation tracking (CFT) problem for networked perturbed robotic systems (NPRSs) under directed graph information interaction, considering parametric uncertainties, external perturbations, and actuator input deadzone. To address this complex problem, a novel hierarchical fixed-time neural adaptive control algorithm is proposed based on a hierarchical fixed-time framework and a neural adaptive control strategy. The objective of this study is to achieve accurate CFT of NPRSs within a fixed time. Specifically, we design a distributed observer algorithm to estimate the states of the virtual leader within a fixed time accurately. By using these observers, a neural adaptive fixed-time controller is developed in the local control layer to ensure rapid and reliable system performance. Through the use of the Lyapunov argument, we derive sufficient conditions on the control parameters to guarantee the fixed-time stability of NPRSs. The theoretical results are eventually validated through numerical simulations, demonstrating the effectiveness and robustness of the proposed approach.

Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators

This paper studies the fixed-time fuzzy adaptive self-triggered control of n-link robotic manipulators. To achieve fixed-time stability, a fuzzy adaptive fixed-time control algorithm is proposed by reconstructing the self-triggered controller and using the singularity-free function, which avoids the singularity problem and obtains fixed-time stability. Meanwhile, the self-triggered mechanism reduces the communication resources between the actuator and the controller, improving the system's transmission efficiency. Through the above thoughts, a kind of fixed-time fuzzy adaptive controller based on the self-triggered mechanism is designed, which guarantees that the tracking error of each joint converges to the prescribed range within a fixed time. Finally, the effectiveness of the proposed algorithm is verified by a simulation example of the two-link robotic manipulator.

Fuzzy adaptive fixed-time control for output-constrained uncertain nonstrict-feedback time-delay systems

This paper deals with the problem of fuzzy adaptive fixed-time control for a class of uncertain nonlinear nonstrict feedback systems with time delays and output constraints. The negative effects of time delays on system performance and stability are overcome by introducing a new Barrier Lyapunov–Krasovskii (BLK) function and an innovative inequality. In addition, the singularity problem that arises in the process of deriving the control and adaptive laws, is solved by the proposed BLK function. The controller is designed in the backstepping framework which ensures that the system output does not violate predefined constraints. The proposed controller needs less information from the system and therefore has less implementation complexity than previous references, which leads to a more straightforward implementation. A fuzzy system approximation is utilized to overcome the uncertainties of the model. It is guaranteed that all closed-loop system signals converge to small neighborhoods around zero in a fixed time. Finally, an example is presented to verify that the proposed method achieves the control objectives.

Adaptive Fixed-time Control for Multiple Switched Coupled Neural Networks

Adaptive Fixed-time Control for Multiple Switched Coupled Neural Networks

Adaptive fixed-time difference synchronization for different classes of chaotic dynamical systems

This article examines adaptive fixed-time difference synchronization for various classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in this article to investigate the difference synchronization for the Sprott chaotic system, both with and without delay. The fixed settling time (T) has been estimated successfully. It is also shown that the trajectories of error states approach to the origin within a fixed time (T). The theoretical analysis is validated by simulating Sprott chaotic systems both with and without delay. On the other hand, various nonlinear chaotic systems are explored for difference synchronization in discrete chaotic systems. Several chaotic maps, including Tinkerbell, Henon, and Hitzl-Zele, have been used to achieve synchronization in these discrete systems. The numerical results are presented graphically, verifying the theoretical outcomes of difference synchronization for various classes of chaotic dynamical systems.

Antisaturation fixed-time backstepping fuzzy integral sliding mode control for automatic landing of fixed-wing unmanned aerial vehicles

This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.

Dynamic Event-Based Adaptive Fixed-Time Control for Uncertain Strict-Feedback Nonlinear Systems With State Constraints.

In this article, the event-triggered fixed-time tracking control is investigated for uncertain strict-feedback nonlinear systems involving state constraints. By employing the universal transformed function (UTF) and coordinate transformation techniques into backstepping design procedure, the proposed control scheme ensures that all states are constrained within the time-varying asymmetric boundaries, and meanwhile, the undesired feasibility condition existing in other constrained controllers can be removed elegantly. Different from the existing static event-triggered mechanism, a dynamic event-triggered mechanism (DETM) is devised via constructing a novel dynamic function, so that the communication burden from the controller to actuator is further alleviated. Furthermore, with the aid of adaptive neural network (NN) technique and generalized first-order filter, together with Lyapunov theory, it is proved that the states of closed-loop system converge to small regions around zero with fixed-time convergence rate. The simulation results confirm the benefits of developed scheme.

Adaptive fixed-time tracking control for nonlinear systems subject to asymmetric input saturation

For nonlinear systems with asymmetric input saturation, an adaptive fixed-time control strategy via multi-dimensional Taylor network (MTN) is proposed to effectively solve the tracking control problem. Firstly, the Gaussian error function and the differential mean value theorem are used to simulate the asymmetric input saturation model, that is, the nonlinear model is transformed into a linear model with a bounded perturbation. Secondly, MTNs are applied to control the design process, which approximate the nonlinear structures with linear combination of polynomials. Thirdly, in addition to the tracking error converging to an arbitrarily small neighborhood around the origin within a fixed time, the proposed control scheme not only guarantees that any signal in the controlled system remains bounded, but also avoids the problem of finite-time control relying on the initial state. Finally, three examples are used to validate the feasibility and superiority of the scheme.

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Adaptive Fixed-Time Control for High-Order Nonlinear Systems With Unknown Control Coefficients and Quantized Input

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case

Adaptive Neural Fixed-Time Control for Uncertain Nonlinear Systems

The article addresses the adaptive fixed-time system control problem subject to unknown nonlinear functions. By employing backstepping technique, fixed-time control, and neural networks (NNs), an adaptive fixed-time control approach is developed. NNs are utilized to package the unknown nonlinearities in the controlled system. The hyperbolic tangent functions are firstly utilized to solve the singular problem, which may exist in the derivation of virtual controller. Meanwhile, the jitter phenomenon is avoided. The developed controller design scheme not only assures the signals’ boundedness within fixed-time interval, but also makes the tracking error converge. Finally, on the aid of the simulation results, the effective of the designed control technique is shown.

A generalized super-twisting algorithm-based adaptive fixed-time controller for spacecraft pose tracking

Abstract A generalized super-twisting second-order sliding mode adaptive fixed-time control law, which is used for spacecraft pose tracking in the presence of internal and external uncertainties, is proposed. Lie group SE(3) (for special Euclidean group), which is the configuration space for rigid body motion, is used for modeling the six-degrees-of-freedom dynamics of spacecraft. A fixed-time sliding mode surface is proposed and applied to design an generalized super-twisting sliding mode control law. A novel dual-layer adaption law for the controller is proposed to the ensure the gains varying rapidly with the disturbance. The adaptive second-order sliding mode controller guarantees a uniform exact convergence for the closed-loop tracking control system with less energy consumption. Numerical simulations are performed to demonstrate the excellent performances of the control law.

Neural-Network-Based Adaptive Fixed-Time Control for a 2-DOF Helicopter System With Input Quantization and Output Constraints.

This study proposes a neural-network (NN)-based adaptive fixed-time control method for a two-degree-of-freedom (2-DOF) nonlinear helicopter system with input quantization and output constraints. First, a hysteresis quantizer is employed to mitigate chattering during signal quantization, and adaptive variables are utilized to eliminate errors in the quantization process. Subsequently, the system uncertainties are approximated using a radial basis function NN. Simultaneously, a logarithmic barrier Lyapunov function (BLF) is constructed to prevent the system outputs from violating the constraint boundaries. Based on a rigorous Lyapunov stability analysis and the fixed-time stability criterion, the signals of the closed-loop system are proven to be bounded within a fixed time. Finally, numerical simulations and experiments verified the feasibility of the proposed method.

Neural-Network-Based Adaptive Fixed-Time Control for Nonlinear Multiagent Non-Affine Systems.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

Nonlinear system controlled using novel adaptive fixed-time SMC

<abstract><p>This work introduces a novel adaptive fixed-time control strategy for nonlinear systems subject to external disturbances. The focus pertains to the introduction of the fixed-time terminal sliding mode control (FxSMC) technique. The proposed scheme exhibits rapid convergence, chatter-free and smooth control inputs, and stability within a fixed time. The utilization of an adaptive methodology in combination with the FxSMC yields the proposed strategy. This approach is employed to address the dynamic system in the presence of external disturbances. The results obtained from the Lyapunov analysis will provide insights into the stability of the closed-loop system in a fixed time. In the end, the simulation results are presented in order to assess and demonstrate the effectiveness of the methodology.</p></abstract>

Adaptive Fixed-Time Control Strategy of Generator Excitation and Thyristor-Controlled Series Capacitor in Multi-Machine Energy Systems

Adaptive Fixed-Time Control Strategy of Generator Excitation and Thyristor-Controlled Series Capacitor in Multi-Machine Energy Systems

Saturation-Tolerant Adaptive Fixed-Time Control of Underactuated Surface Vessel With Improved Given Performances

Saturation-Tolerant Adaptive Fixed-Time Control of Underactuated Surface Vessel With Improved Given Performances

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Vision-based adaptive fixed-time uncooperative target tracking for QUAV with unknown disturbances

This article investigates the problem of the vision-based uncooperative target tracking control for a quadrotor unmanned aerial vehicle (QUAV) with unknown external disturbances. Note that the uncooperative target information cannot be obtained directly and need to be measured by a monocular sensor installed on the QUAV. In the light of the monocular sensor, a vision-based adaptive fixed-time control scheme is constructed to deal with the uncooperative target tracking problem. To efficiently observe unknown external disturbances, a fixed-time disturbance observer (FTDO) is designed by using the super-twisting (ST) algorithm. Finally, with the help of the Lyapunov stability theory, which guarantees the boundedness of all closed-loop signals, the QUAV is capable of tracking the uncooperative target in fixed time. The results of the simulation demonstrate the effectiveness of the proposed control strategy.

Fixed-time adaptive tracking control of two moving targets for a class of non-linear multi-agent systems

In this research paper, the fixed-time adaptive tracking of two moving targets for a class of unknown non-linear multi-agent systems based on a distributed competition approach is studied. Each agent simultaneously participates in two competitions based on the k-Winner Take All (k-WTA) approach to obtain its allocation status. Using a mean value estimator, the agent can calculate its allocation status only by its neighbor's information. Since an agent can only track one target, an extended tracking error is introduced, where if the agent wins one of the competitions, it will track the assigned target, and if the agent wins both competitions, by selecting one of the targets, track the selected target. Also, the agent which is not win any competitions, return to a specified point. Then, using neural networks and adaptive techniques, an adaptive fixed-time controller is introduced for the agents to track the target based on the allocation status or to return to the specified point. Analysis of the stability of the closed-loop system through the Lyapunov theorem is investigated. Finally, a simulation study to show the efficiency of the theoretical results is presented.